Properties

Label 2.25.ap_dw
Base Field $\F_{5^2}$
Dimension $2$
$p$-rank $0$
Principally polarizable
Does not contain a Jacobian

Learn more about

Invariants

Base field:  $\F_{5^2}$
Dimension:  $2$
Weil polynomial:  $( 1 - 5 x )^{2}( 1 - 5 x + 25 x^{2} )$
Frobenius angles:  $0.0$, $0.0$, $\pm0.333333333333$
Angle rank:  $0$ (numerical)

Newton polygon

This isogeny class is supersingular.

$p$-rank:  $0$
Slopes:  $[1/2, 1/2, 1/2, 1/2]$

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 336 374976 244109376 152343749376 95275917959376 59589387451109376 37251472497558359376 23283004760742187109376 14551915228359222412109376 9094946086406707763662109376

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 11 601 15626 390001 9756251 244078126 6103281251 152587500001 3814697265626 95367421875001

Decomposition

1.25.ak $\times$ 1.25.af

Base change

This is a primitive isogeny class.